Abstract
Rough sets are described by an approach using possible coverings in an incomplete information table with similarity of values. Lots of possible coverings are derived in an incomplete information table. This seems to cause difficulty due to computational complexity, but it is not, because the family of possible coverings has a lattice structure. Four approximations that make up a rough set are derived by using only two coverings: the minimum and maximum possible ones which are derived from the minimum and the maximum possible indiscernibility relations that are equal to the intersection and the union of those from possible tables. The approximations are equal to those derived using the minimum and the maximum possibly indiscernible classes.
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Notes
- 1.
Unless confusion may arise, \(R_{a_{i}}\) is used.
- 2.
\(\delta \) is used in place of \(\delta _{a_{i}}\) if no confusion arises.
- 3.
Therefore, \(R_{a_{i}}^{\delta }\) becomes a tolerance relation.
- 4.
C(o) or \(C(o)_{a_{i}}\) is used in place of \(C(o)_{a_{i}}^{\delta }\) if no confusion arises.
- 5.
\(\sqsubseteq \) is defined as \(\mathcal{E} \sqsubseteq \mathcal{E'}\) if \(\forall E \in \mathcal{E} \exists E' \in \mathcal{E'} \wedge E \subseteq E'\).
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Nakata, M., Saito, N., Sakai, H., Fujiwara, T. (2021). Possible Coverings in Incomplete Information Tables with Similarity of Values. In: Ramanna, S., Cornelis, C., Ciucci, D. (eds) Rough Sets. IJCRS 2021. Lecture Notes in Computer Science(), vol 12872. Springer, Cham. https://doi.org/10.1007/978-3-030-87334-9_7
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DOI: https://doi.org/10.1007/978-3-030-87334-9_7
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